Chiral symmetry restoration at finite temperature in the linear sigma-model

Abstract

The temperature behaviour of meson condensates 〈σ 0〉 and 〈σ 8〉 is calculated in the SU (3) × SU (3)-linear sigma model. The couplings of the Lagrangian are fitted to the physical π, K, η, η′ masses, the pion decay constant and a O + ( I = 0) scalar mass of m σ = 1.5 GeV. The quartic terms of the mesonic interaction are converted to a quadratic term with the help of a Hubbard-Stratonovich transformation. Effective mass terms are generated this way, which are treated self-consistently to leading order of a 1 N -expansion. We calculate the light 〈 q ̄ q〉 and strange 〈 s ̄ s〉 quark condensates using PCAC relations between the meson masses and condensates. For a cut-off value of 1.5 GeV we find a first-order chiral transition at a critical temperature T c ∼ 161 MeV. At this temperature the spontaneously broken subgroup SU(2) × SU(2) is restored. Entropy density, energy density and pressure are calculated for temperatures up to and slightly above the critical temperature. To our surprise we find some indications for a reduced contribution from strange mesons for T ⩾ T c .